Mitochondrial DNA (mtDNA) is useful to assist with identification of the source of a biological sample, or to confirm matrilineal relatedness. Although the autosomal genome is much larger, mtDNA has an advantage for forensic applications of multiple copy number per cell, allowing better recovery of sequence information from degraded samples. In addition, biological samples such as fingernails, old bones, teeth and hair have mtDNA but little or no autosomal DNA. The relatively low mutation rate of the mitochondrial genome (mitogenome) means that there can be large sets of matrilineal-related individuals sharing a common mitogenome. Here we present the mitolina simulation software that we use to describe the distribution of the number of mitogenomes in a population that match a given mitogenome, and investigate its dependence on population size and growth rate, and on a database count of the mitogenome. Further, we report on the distribution of the number of meioses separating pairs of individuals with matching mitogenome. Our results have important implications for assessing the weight of mtDNA profile evidence in forensic science, but mtDNA analysis has many non-human applications, for example in tracking the source of ivory. Our methods and software can also be used for simulations to help validate models of population history in human or non-human populations.